Journal of Computational Physics
Journal of Computational Physics
Iterative solution methods
Discretization on non-orthogonal, quadrilateral grids for inhomogeneous, anisotropic media
Journal of Computational Physics
The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Discretization on quadrilateral grids with improved monotonicity properties
Journal of Computational Physics
Monotonicity of control volume methods
Numerische Mathematik
A Multipoint Flux Mixed Finite Element Method
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
Monotonic solution of heterogeneous anisotropic diffusion problems
Journal of Computational Physics
Hi-index | 31.46 |
A new family of flux-continuous, locally conservative, finite-volume schemes is presented for solving the general tensor pressure equation of subsurface flow in porous media. The new schemes have full pressure continuity imposed across control-volume faces. Previous families of flux-continuous schemes are point-wise continuous in pressure and flux. When applying the earlier point-wise flux-continuous schemes to strongly anisotropic full-tensor fields their failure to satisfy a maximum principle (as with other FEM and finite-volume methods) can result in loss of local stability for high anisotropy ratios which can cause strong spurious oscillations in the numerical pressure solution. An M-matrix analysis reveals the upper limits for guaranteeing a maximum principle for general 9-point schemes and aids in the design of schemes that minimize the occurrence of spurious oscillations in the discrete pressure field. The full pressure continuity schemes are shown to possess a larger range of flux-continuous schemes, than the previous point-wise counter parts. For strongly anisotropic full-tensor cases it is shown that the full quadrature range possessed by the new schemes permits these schemes to exploit quadrature points (previously out of range) that are shown to minimize spurious oscillations in discrete pressure solutions. The new formulation leads to a more robust quasi-positive family of flux-continuous schemes applicable to general discontinuous full-tensor fields.